Pollutant transport includes both advection and sub-grid scale diffusion. Advection has to do with pollutant transport due to the mean wind fields, and diffusion involves sub-grid scale turbulent mixing of pollutants. If a plume is transported primarily by advection, then it may travel a long distance without much change in pollutant concentrations. On the other hand, if a plume is transported primarily by diffusion, then the pollutants will mix more quickly and nearer to the source, which will result in substantial changes to pollutant concentrations.

In CCTM, the advection process is divided into horizontal and vertical components. This distinction is possible because mean atmospheric motion is mostly horizontal. Often, the vertical motion is related to the interaction of dynamics and thermodynamics. The advection process relies on the mass conservation characteristics of the continuity equation. Data consistency is maintained for air quality simulations by using dynamically and thermodynamically consistent meteorology data from MCIP. When the meteorological data and the numerical advection algorithms are not exactly mass consistent, one needs to solve a modified advection equation (Byun, 1999). A new mass continuity scheme, similar to that used in the air quality forecasting version of CMAQ, has been implemented for the 2005 release. This scheme is globally mass-conserving and uses the piecewise parabolic method (PPM) (Colella and Woodward, 1984) advection scheme for horizontal advection, deriving a vertical velocity component at each grid cell that satisfies the mass continuity equation using the driving meteorology model's air density. The mixing ratio correction step, used in previous CMAQ versions, is not needed with this method. Note that, the former advection scheme, with the same horizontal advection but also using PPM for the vertical velocity component, is still available, along with the mixing ratio correction step.

The horizontal advection module for CMAQ is the Piecewise-Parabolic Method (PPM) (Colella and Woodward, 1984). This algorithm is based on the finite volume subgrid definition of the advected scalar. In PPM, the subgrid distribution is described by a parabola in each grid interval. PPM is a monotonic and positive definite scheme. Positive definite schemes maintain the sign of input values, which means, in this case, that positive concentrations will remain positive and cannot become negative.

The vertical advection modules solve for the vertical advection with no mass-exchange boundary conditions at the bottom or top of the model. CMAQ also uses PPM as its vertical advection module. In CCTM, the PPM algorithm with a steepening procedure is implemented for vertical advection as the default because of the strong gradients in the tracer species that are observed in photochemical air quality conditions.

In CCTM, turbulent fluxes are expressed in terms of the mixing ratios and an air-density-weighted Jacobian to handle atmospheric diffusion processes with generalized coordinates. This approach is convenient for numerically solving the flux-form turbulence mixing because most flux-based closure algorithms use parameterizations of turbulent fluxes of conserving quantities, such as mass mixing ratios. In CMAQ version 4.5, Eddy diffusion is implemented for representing vertical diffusion. Eddy diffusivity is a local mixing scheme and is estimated using the same planetary boundary layer (PBL) similarity-based algorithm as in the Regional Acid Deposition Model, RADM, (Chang et al., 1987, 1990). In CCTM, the deposition process is simulated as a flux boundary condition that affects the concentration in the lowest layer. By treating the deposition process as the loss of mass due to the diffusion flux at the bottom of the model, one can relate the bottom boundary condition in the generalized coordinate system to that in the Cartesian coordinate system. Version 4.5 has an improved version of the minimum allowable vertical eddy diffusivity. The new version interpolates between urban and non-urban land cover allowing a larger minimum value for a larger fraction of urban land cover.

In CMAQ version 4.5 horizontal diffusion is implemented with a single eddy diffusion algorithm that is based on local wind deformation and is scaled to the grid cell size. The horizontal eddy diffuseness is assumed to be uniform but dependent on the grid size of the model. The diffusivity is larger for a higher resolution run where the numerical diffusion due to the advection process is smaller.